Rework Problem 12-30 using the modified large-sample approach described in Section 12-7.2. Compare the two sets of confidence intervals obtained and discuss.

Problem 12-30

Consider the variance components in the random model from Problem 12-9.

(a) Find an exact 95 percent confidence interval on σ².

(b) Find approximate 95 percent confidence intervals on the other variance components using the Satterthwaite method.

Problem 12-9.

An experiment was performed to investigate the capability of a measurement system. Ten parts were randomly selected, and two randomly selected operators measured each part three times. The tests were made in random order, and the data below resulted.

 

Operator 1 Measurements Operator 2 Measurements Part Number 1 3 1 3 50 49 50 50 48 51 1 2 52 52 51 51 51 51 53 50 50 54 52 51 3 49 51 50 48 50 51 4 48 49 48 48 49 48 52 50 50 52 50 50 7 51 51 51 51 50 50 8 52 50 49 53 48 50 9 50 51 50 51 48 49 47 46 49 46 47 48 10